Integral equations, calculus of variations and its applications R10QV7GHVG

URI	`m2://res/R10QV7GHVG`
Kind	course
Creators	D. N Pandey (instructor), P.N. Agarwal (instructor)
Date	2017-07-16
Scope	in
Ids	course 00582g326:111107103

Expressions

e1: edition

Language	en
Date	2017-07-16

m1: page, IIT Roorkee (record). nptel 111107103
m2: page, 2017-07-16 (record). nptel 111107103

Contents

part 1: Unit-1
session 1: Definition and classification of linear integral equations
session 2: Conversion of IVP into integral equations
session 3: Conversion of BVP into an integral equations
session 4: Conversion of integral equations into differential equations
session 5: Integro-differential equations
part 2: Unit-2
session 6: Fredholm integral equation with separable kernel: Theory
session 7: Fredholm integral equation with separable kernel: Examples
session 8: Solution of integral equations by successive substitutions
session 9: Solution of integral equations by successive approximations
session 10: Solution of integral equations by successive approximations: Resolvent kernel
part 3: Unit-3
session 11: Fredholm integral equations with symmetric kernels: Properties of eigenvalues and eigenfunctions
session 12: Fredholm integral equations with symmetric kernels: Hilbert Schmidt theory
session 13: Fredholm integral equations with symmetric kernels: Examples
session 14: Construction of Green function-I
session 15: Construction of Green function-II
part 4: Unit-4
session 16: Green function for self adjoint linear differential equations
session 17: Green function for non-homogeneous boundary value problem
session 18: Fredholm alternative theorem-I
session 19: Fredholm alternative theorem-II
session 20: Fredholm method of solutions
part 5: Unit-5
session 21: Classical Fredholm theory: Fredholm first theorem-I
session 22: Classical Fredholm theory: Fredholm first theorem-II
session 23: Classical Fredholm theory: Fredholm second theorem and third theorem
session 24: Method of successive approximations
session 25: Neumann series and resolvent kernels-I
part 6: Unit-6
session 26: Neumann series and resolvent kernels-II
session 27: Equations with convolution type kernels-I
session 28: Equations with convolution type kernels-II
session 29: Singular integral equations-I
session 30: Singular integral equations-II
part 7: Unit-7
session 31: Cauchy type integral equations-I
session 32: Cauchy type integral equations-II
session 33: Cauchy type integral equations-III
session 34: Cauchy type integral equations-IV
session 35: Cauchy type integral equations-V
part 8: Unit-8
session 36: Solution of integral equations using Fourier transform
session 37: Solution of integral equations using Hilbert transform-I
session 38: Solution of integral equations using Hilbert transform-II
session 39: Calculus of variations: Introduction
session 40: Calculus of variations: Basic concepts-I
part 9: Unit-9
session 41: Calculus of variations: Basic concepts-II
session 42: Calculus of variations: Basic concepts and Euler equation
session 43: Euler equation: Some particular cases
session 44: Euler equation : A particular case and Geodesics
session 45: Brachistochrone problem and Euler equation-I
part 10: Unit-10
session 46: Euler's equation-II
session 47: Functions of several independent variables
session 48: Variational problems in parametric form
session 49: Variational problems of general type
session 50: Variational derivative and invariance of Euler's equation
part 11: Unit-11
session 51: Invariance of Euler's equation and isoperimetric problem-I
session 52: Isoperimetric problem-II
session 53: Variational problem involving a conditional extremum-I
session 54: Variational problem involving a conditional extremum-II
session 55: Variational problems with moving boundaries-I
part 12: Unit-12
session 56: Variational problems with moving boundaries-II
session 57: Variational problems with moving boundaries-III
session 58: Variational problems with moving boundaries; One sided variation
session 59: Variational problem with a movable boundary for a functional dependent on two functions
session 60: Hamilton's principle: Variational principle of least action

Catalogue records

nptel: 111107103 (manifestation)
nptel_video: 111107103 (manifestation)